Plotting a complex exponential, exp(i*x), in 3D?

Hi, I try to plot the complex exponential, exp(i*x), in 3D. As in https://qph.is.quoracdn.net/main-qimg-b7ac15119bfa0a4840084c98da915ed8?convert_to_webp=true. Using plot or fplot, I got the warning "Imaginary parts of complex X and/or Y arguments ignored" and with ezplot: "This function has no real values".

Any suggestions on how to make such a plot in Matlab?

Thanks, Steven

Answer 1

[Star Strider]

This approximates it:

t = linspace(0, 2.5, 250);
f = exp(2*pi*4/2.5*1i*t);

figure(1)
plot3(t, real(f), imag(f), 'LineWidth',2)
hold on
plot3(t, real(f), zeros(size(t))-1.5)
plot3(t, zeros(size(t))-2, imag(f))
hold off
grid on
axis([-1  3    -2  2    -1.5  1.5])
view([-125  30])
xlabel('Time', 'Rotation',-30)
ylabel('Real Axis', 'Rotation',10)
zlabel('Imag Axis')

If you want to add the labels, see the documetation for the text function.

[Steven]

Great! Many, many thanks!

[Star Strider]

My pleasure!

This was a fun problem for me!

[appala naidu k]

Dear sir, Can you please help to plot the same graph for exponential decay and rise?

[Star Strider]

Just multiply the exponential term with it.

t = linspace(0, 2.5, 250);
f = exp(2*pi*4/2.5*1i*t);
e = exp(-0.5*t);
fe = f .* e;

figure(1)
plot3(t, real(fe), imag(fe), 'LineWidth',2)
hold on
plot3(t, real(fe), zeros(size(t))-1.5)
plot3(t, zeros(size(t))-2, imag(fe))
hold off
grid on
axis([-1  3    -2  2    -1.5  1.5])
view([-125  30])
xlabel('\leftarrow Time', 'Rotation',-30)
ylabel('Real Axis', 'Rotation',10)
zlabel('Imag Axis')

Make appropriate changes to get different results.

.

Answer 2

[Steven Lord]

 x = 0:0.1:10;
 yz = exp(1i*x);
 plot3(x, real(yz), imag(yz))
 ylabel('\Re(e^{1i*x})');
 zlabel('\Im(e^{1i*x})');